学术活动

On the size of permutation balls with the infinity norm-Prof. Moshe Schwartz （Ben-Gurion University of the Negev）

作者： 来源： 时间：2017-09-07

题目：On the size of permutation balls with the infinity norm

报告人：Prof. Moshe Schwartz （Ben-Gurion University of the Negev）

Abstract：

One of the main goals of coding theory is to study problems of ball-packing in different metric spaces. These spaces are usually the Hamming-cube, the Jonhson graph, grids with the /ell_1-metric, and even Grassmannians. Recently, motivated by application to flash memories, the symmetric group, S_n, endowed with the infinity norm, has gained interest. Surprisingly, unlike many other spaces, the asymptotic size of balls in this space is unknown. The known lower and upper bounds are far apart.

In this talk I will describe several results on the subject. The first will be an exact solution for the case of a fixed radius r, and n tending to infinity. The second will be a study of the case of radius r linear in n. The main tool we use is a study of permanents of (0,1) matrices with appropriate constraints. Some interesting connections between this combinatorial counting problem and formal languages will be highlighted as well.

The talk is based on joint work with Itzhak Tamo, Yonatan Yehezkeally, and Pascal Vontobel.